Mode-converted Electron Bernstein Waves Francesco Volpe currently at Dept of Applied Physics and Applied Mathematics Columbia University, New York Presentation prepared while at Engineering Physics Dept University of Wisconsin, Madison Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 1
Outline Motivation: Someone likes it hot and overdense Principle of EBWs and Mode Conversions EBWs in This Talk Madison World Stellarator W7-AS HSX CHS, Heliotron, LHD, WEGA Sph.Tokamak MAST Pegasus Mini-RT, NSTX Tokamak TCV DIII-D? RFP RFX-mod MST Summary & Conclusions Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 2
Motivation for Electron Bernstein Waves Several MCF plasmas are too dense or have too low magnetic field for conventional Electron Cyclotron Resonant Heating (ECRH) EBWs do not suffer from upper density limits Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 3
Electron Bernstein waves Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 4
Marine waves are another example of gyrophase organization Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 5
x OXB-Scheme: special view makes modes degenerate and not evanescent In the real space In the phase space (w p /w) 2 1 Slow X L O-wave cut-off x O L B 0 sin 2 f=n 2 z,opt=y/(y+1), Y=w c /w z Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 6
OXB-Scheme: O-X conversion Airy O SX Merging of O and SX waves when their cutoffs overlap: even odd Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 7
SX-B mode conversion Finite Larmor radius 6th order correction to Booker quartic Deflection from UHR and Propagation at X>1 (overdense), until Cyclotron damping Conversion efficiency can be limited by: - Collisional damping (if edge cold) - Back-tunneling SX-FX (if barrier thin) - Parametric decay (at high power) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 8
FX-(SX)-B Conversion is a Tunnel Effect X-wave damped Unlike OXB, evanescent layer always has finite thickness. Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 9
Mode conversions are ubiquitous wave phenomena at medium interfaces. Example: seismic waves Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 10
Mode conversions are ubiquitous wave phenomena at medium interfaces. Example: seismic waves Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 11
EBW Emission, Heating & CD in the W7-AS Stellarator (with H.P. Laqua) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 12
Antenna Max Transmission Min Doppler effects Pure O-mode detection Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 13
Oblique view elliptic polarization phase-shifter needed l/4 phase shifter polarization rotator Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 14
Broadband phase shifter Requirements: Phase shift f=90 0 8 0 ( 2% intensity) Frequency band f=66-78ghz Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 15
Test quasi-optical components Antenna Polarizer Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 16
Heterodyne radiometer 24 channel ECE heterodyne radiometer, f=63-78ghz + 16 channel Zoom Df=4GHz, f LO adjustable + 8 new fixed channels After several amplifiers and Power-splitters... B IF =300MHz B video 1MHz spatial resolution 1cm temporal resolution 2ms Independent acquisition for 70 and 140GHz radiometer Overlap: ECE (X2) n e <1.2 10 20 m -3 EBE (B1) n e > 6 10 19 m -3 Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 17
Ray tracing 5th order Runge-Kutta dr D / N d w D / w dn D / r d w D / w D=Det(e ij +N i N j -N 2 d ij ), e=hot diel.tensor OX: 1) optimization of injection angle, 2) symmetries in narrow evanescent layer XB: Ridder s method to correct N Full stellarator geometry Poloidal component Off-midplane launch Toroidal curvature Broken axisymmetry Parallel computing on 16 workstation cluster Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 18
EBE Spectrum and Profile n e from TS and Li-Beam } mapping f r B from equilibrium code TRANS Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 19
Heat Waves: EB-diagnostic during EB-heating Problem: EBH Parametric decay Non-thermal peaks f pump nf LH (n=1,2,...) Overlapped thermal spectrum cannot be measured at the same harmonic Solution: EBH 2nd harm. & EBE 1st harm. Plasma has to be O2-overdense (at least n e >2.4 10 20 m -3, recently n e 4 10 20 m -3 ) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 20
Confinement Transition EBE edge EBE core H-Mode Threshold often exceeds ECE cutoff: H a Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 21
Edge-localized Modes Cross-correlation with H a : Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 22
Radiative Collapse T Hysteresis? f q ~n e n imp Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 23
Due to oblique injection, OXB heating also drives current! Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 24
Angle is fixed by OXB, but co/ctr-cd can be selected and N adjusted by varying the magnetic configuration Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 25
EBW Emission & Heating in the MAST Spherical Tokamak (with V. Shevchenko) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 26
2D-steerable, multi-beam antenna allowed simultaneous EBW emission and heating Mirror 5 Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 27
Emission in a spherical tokamak is banded as a consequence of low aspect ratio R-cutoff L-cutoff UHR Plasma Resonance 5 w ce 4 w ce 3 w ce 2 w ce Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 28
EBE evidenced fast electrons at sawtooth crashes D a Soft-X Rays EBE 60.5GHz 62.5GHZ 63.5GZ 66.5GHz Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 29
2D angular scans of EBW emission indicated optimal direction for heating at MAST spherical tokamak 1.0 f=60.5ghz, = -5.6deg 1.0 f=60.5ghz, f = -7deg BXO-EBW Signal (a.u.) 0.8 0.6 0.4 0.2 0.0-11 -10-9 -8-7 -6-5 Toroidal angle (deg) Identified optimal launch direction for BXO-EBW Signal (a.u.) 2.5 o FWHM 1.2 o FWHM first OXB heating in a spherical tokamak In spite of non-optimal frequency (60GHz) and alignment issues 0.8 0.6 0.4 0.2 0.0-7 -6-5 -4 ECRH Power Total Energy Poloidal angle (deg) 7 kj (~ 0.25 MW) 60 kj (~3 MW) 250 kw Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 30
2D angular scans confirmed that emission is anisotropic New q-profile diagnostic concept Plasma O-mode n e B total O-mode Inclination of conversion contours at various f gives Inclination of field line at various radial positions Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 31
Special design allows tilted mirror to spin at 12,000rpm and scan EBW emission within the same discharge Self-balanced design spins at 12,000rpm 3.3585 tonnes 3.3585 tonnes First measurements carried out. Analysis under way. Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 32
EBW Heating in the TCV Tokamak (with A. Mϋck, L. Curchod, A. Pochelon et al.) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 33
Angular Scan of EBW injection shows min stray (max conversion) close to calculated optimum Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 34
Stray radiation correlates with ELMy phases, consistently with reduced conversion efficiency Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 35
SXR during pulsed EBWH was complicated by sawteeth Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 36
Long, more central (r~0.4) EBWH resulted in clear bigger-than-sawtooth T e increase T e builds over e ~50ms Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 37
Modeling of EBW Current Drive in the RFX-mod RFP (with R. Bilato and A. Köhn) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 38
For RFX-mod values of n e and T e at EBW deposition for 28GHz, 100kW absorbed should drive ~10kA, sufficient to improve confinement Steady state Localization Position control Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 39
Harmonics of ~11GHz are best for Current Drive at reversal layer of 1MA RFX-mod plasmas Analytic Equilibrium: Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 40
Magnetic configuration of RFP has some peculiarities 1. B almost poloidally symmetric, doesn t scale as 1/R Any launching position is Low Field Side (LFS). No High Field Side (HFS) schemes, e.g. no SX-B. 2. low B low w ce low w long vacuum wavelength λ cutoffs and resonances close to each other within few λ tunneling Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 41
FX-B is unsuitable for RFX-mod Equilibrium at 1MA f>11ghz, e.g. f=28ghz l=1cm L n =2cm Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 42
Injection along a vertical port, slightly tilted, is optimal Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 43
Further waist optimization leads to 58% efficiency Limiting factors to higher efficiency: curvature mismatch (included) fluctuations (not included) Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 44
n e and B fluctuations reduce conversion efficiency OXB n e fluctuations at O-mode cutoff a) cutoff is corrugated incidence on cutoff locally non-optimal reduced OX conversion efficiency b) cutoff moves optimal angle changes with time mode conversion efficiency fluctuates in time B fluctuations at O-mode cutoff optimal angle fluctuates according to N z,opt2 = w ce /(w ce +w) FX-B n e and B fluctuations at FX-mode cutoff and UHR their positions and thus thickness of evanescent layer in between fluctuates Solutions; f/back on direction or, easier, on w longer wavelength for easier tunneling higher frequency for deeper cutoff, in less turbulent region Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 45
Alf s full-wave code Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 46
Full-wave code reconstructs OXB conversion and follows EBWs until their wavelength can be resolved by grid R or FX cutoff UH resonance P or O cutoff L or SX cutoff Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 47
Multiple reflections by graphite wall re-inject some power and increase overall OXB efficiency to 67% Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 48
Summary and Conclusions Stellarators need EBWs - overdense + Mode-converted EBWs benefit from Stellarator environment - steep gradients, external control of configuration, tolerable n e and B fluctuations = A marriage! EBW heating, emission and CD all proved in W7-AS stellarator In spite of 60GHz being too high, EBW heating succeded also in MAST, - after scenario optimization (steep gradients) - and guidance from EBW emission (optimal direction). Spinning mirror provided angular scans of OXB conversion efficiency every 10ms possible q-profile diagnostic. EBW heating also proved in TCV tokamak EBW CD at edge of RFX-mod RFP plasma might trigger tranport barrier Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 49
Long-term (power-plant and CTF) applications of EBWs Stellarators: compensation for undesired bootstrap current at high b. Sph.Tokamaks: Non-inductive start-up and growth of a target for NBI. Current profile tailoring. Tokamaks: T e diagnosis of ITER divertor region? Not overdense, but Upper Hybrid resonant layer (thus, EBWs) exists. RFPs: Improved confinement by suppressing MHD and triggering transport barriers at reversal layer. Talk at IAE, Kyoto University July 30, 2012 Mode-converted Electron Bernstein Waves (F. Volpe) 50